Global Strong and Weak Solutions to the Initial-boundary-value Problem of 2D Compressible MHD System with Large Initial Data and Vacuum

2021/05/11 by Yazhou Chen, Bin Huang, Chen, Yazhou +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2105.11291

openalex publication_date 2021/05/11 · openalex created_date 2021/06/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the barotropic compressible magnetohydrodynamic equations with the shear viscosity being a positive constant and the bulk one being proportional to a power of the density in a general two-dimensional bounded simply connected domain. For initial density allowed to vanish, we prove that the initial-boundary-value problem of 2D compressible MHD system admits the global strong and weak solutions without any restrictions on the size of initial data provided the shear viscosity is a positive constant and bulk one is λ=ρ^β with β>4/3. As we known, this is the first result concerning the global existence of strong solutions to the compressible MHD system in general two-dimensional bounded domains with large initial data and vacuum.

Citations

• Existence and Exponential Growth of Global Classical Solutions to the Compressible Navier-Stokes Equations with Slip Boundary Conditions in 3D Bounded Domains
• Global Strong Solutions to the Compressible Magnetohydrodynamic Equations with Slip Boundary Conditions in 3D Bounded Domains

Related

• Global well-posedness for the two dimensional compressible MHD equations with large data
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• Global Strong Solutions to the Cauchy Problem of Three-dimensional Isentropic Magnetohydrodynamics Equations with Large Initial Data
• Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum